Rapid Turnaround of Carotid Artery Simulations

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                                                                             Proposal No.       SI    IIP    CCST

                                             LDRD Proposal

Project Title: Rapid Simulation of Hemodynamic Forces in Carotid Arteries

Investigator(s): Paul F. Fischer                             MCS
ALD(s): F. Fradin

       (1) Funding Profile           TOTAL
              ($K)                     (All      FY2000      FY2000      FY2001       FY2002      FY2003
   Staff/STA Effort
   Post/Pre Doc Effort              150                                 75           75
   Operating Total                  150                                 75           75
(2) Opportunity

During the past two decades, the role of hemodynamics, or fluid mechanics of blood flow, has been
recognized by medical and biological researchers in the development of arterial disease and in the
regulation of cellular biology in both normal and diseased arteries. Vascular disease, including
atherosclerosis, is currently one of the leading causes of death in the United States. The economic impact
of medical treatment of carotid arteries alone is estimated at $60 billion annually.

A number of teams are currently investigating hemodynamic parameters in the genesis of vascular disease,
with computational fluid dynamics (CFD) becoming the most prevalent means of investigation because it
is able to provide more detailed flow information than either in vivo or in vitro experiments.
Computational hemodynamics is at a critical juncture. First, the use of high-resolution imaging
techniques that can provide the geometry and flow rate information necessary for detailed simulations is
becoming more commonplace. Second, parallel numerical software coupled with networks of PCs will
soon be able to provide rapid turn-around of patient-specific simulations. And, finally, the medical
community is beginning to embrace simulation as an analysis tool to better understand disease and
treatment options.

Although it is now possible to simulate flows in patient-specific models of healthy carotid arteries,
numerical simulation studies of flow in diseased carotid are absent from the literature. Flow in diseased
arteries with stenoses (blockage) often exhibit jets that transition to turbulence, making them one to two
orders of magnitude more difficult to simulate than the healthy cases – well beyond the capabilities of
most current hemodynamics codes. Because of our experience with transitional flow simulations in
complex geometries, and access to state of the art parallel computing facilities, Argonne is uniquely
poised to close this gap in detailed understanding of hemodynamic forces acting in diseased carotid
arteries. We have teamed with the biomechanics groups of Prof. F. Loth (UIC) and Dr. H. Bassiouny
(UC) to form a triad comprising numerical, experimental, and medical expertise that can produce
clinically relevant research in this area.

(3) Benefits/beneficiaries/customers
Early results of this work will provide the first detailed computational analysis of unsteady (transitional)
flow in carotid artery bifurcations and thus provide significant insight to clinically relevant hemodynamic
forces in the presence of stenoses. Automated translation of MRI and CT scan images into computational
meshes, coupled with rapid simulation of the hemodynamics, will offer surgeons a new tool to help in
diagnosis and surgical planning. The ultimate goal is to provide a dedicated hardware/software system that
could make wall shear and particle residence time analysis a routine part of off-line patient diagnosis,
much as image inspection by radiologists is today. In addition, this work will advance the state of the art
in high-order numerical methods for simulation of transitional flows in complex geometries, thus
providing DOE with tools for simulating flows in similarly complex passages such as piping and heat
exchanger passages. Software developed in this project will be of use in other flow simulations, such as
the He gas stopper cell currently under development in the ANL ATLAS-ISOL project.

(4) Abstract

We propose to develop CFD technology to provide for rapid turnaround of transitional flow simulations in
patient-specific carotid artery models. The ultimate goal, beyond the scope of this project, is to be able to
provide surgeons with quantitative wall-shear stress and particle residence time predictions within 24
hours of non-invasive MRI or CT imaging in order to aid in the selection of treatment options for the
patient. Such technology requires several ingredients, including automated translation of image scans into
computational meshes, mesh smoothing and optimization, high-order numerical methods, fast elliptic
solvers, advanced parallel algorithms, extensive experimental validation and, possibly, coupling of fluid-
structure interactions. In addition, there is significant medical-biomechanical research that needs to be
undertaken to quantify the impact of known wall-shear stress values on disease progression. Such values
are just now becoming available due to advances in imaging and computing technology. However, no
computations of transitional (weakly turbulent) flows in stenosed areteries have been undertaken. Our
team is poised to be the first to do so. With further participation, we have an opportunity to put Argonne
in the forefront of this research area.

Our simulations will be based on the spectral element method, which, because of its low numerical
dissipation and dispersion, is ideally suited for transitional flow simulations in complex geometries. This
approach provides a significant competitive advantage over current computational hemodynamics codes,
which are based on low-order finite element methods that are appropriate for laminar flows but sub-
optimal for transitional simulations.

We will develop domain-specific automated mesh generation for arterial bifurcations (corresponding to
regions where wall shear stress anomalies and vascular disease are frequently observed). The automated
translation of MRI or CT image slices into spectral element meshes will proceed in three stages. First, a
routine will identify a candidate line defining the intersection of three intersecting planes that trisect the
bifurcation (the “Y”) into independent branches. Second, each branch will be meshed using standard
hexahedral element decompositions for pipes. Third, the recombined mesh will be smoothed using robust
fail-safe mesh optimization techniques. With appropriate objective functions, the entire process can be
iterated hundreds of times on a workstation or PC to provide a suitable mesh in a matter of minutes. It
should ultimately be possible to connect several branches end on end to form a network in the area of
interest. Research in this area will leverage the MCS expertise of L. Freitag, who has developed similar
optimization techniques for tetrahedral-based meshes.

Experimental validation vital for surgical acceptance of our work will be carried out at UIC by the
research team of Prof. F. Loth, Ph.D. Prof. H. Bassiouny, M.D., (UC) will provide CT scan images of in
vivo carotid arteries with stenoses (corresponding to transitional flow cases), along with color Doppler
ultrasound flow rate data. Software developed by Loth will be used to translate the images into rapid
prototype data files from which three-dimensional models can be constructed. These models will be
placed in the flow rig in his laboratory, and detailed velocity distributions will be measured using laser
Doppler anemometry. The same images will be used to generate computational meshes, allowing back to
back comparisons of experiments and simulations.

 Professors Loth and Bassiouny plan to address the outstanding medical research questions through a
sequence of patient imaging and simulation studies. Bassiouny‟s clinic at U. of C. performs 700
ultrasound scans of carotid arteries per year, and he is notified of all cases exhibiting severe stenoses,
which are then investigated further. Loth and Bassiouny propose to undertake a preliminary study of 1-3
patients in the coming year, in order to demonstrate technical feasibility to NIH, followed by a study
involving 10-20 patients over a one-year period, and finally, a study involving roughly 100 patients over a
two- to three-year period. Our goal is to provide the simulation capability for these studies. At the end of
this period we should be well within a factor of five from the 24-hour turn-around goal. Given the
performance of our parallel code (which won the 1999 Gordon Bell Award for demonstrating 380
GFLOPS on 4096 processors), the 24-hour turn-around time could readily be achieved through scaling to
more processors once the viability of this mode of analysis is established. Given the rapidly decreasing
cost of commodity parallel computing, the additional cost for a dedicated cluster of PCs would be a small
fraction of any MRI installation budget.

When one considers that an investigator might typically study 2-3 turbulent simulations in a year, it is
clear that the patient-study schedule outlined above is aggressive, but one that should be feasible. We have
recently undertaken simulations in a model of an arterio-venous (AV) graft, which exhibits a bifurcation
similar to the carotid artery. Figure 1 shows the computational mesh and a close up of vorticity contours,
which reveal the turbulent structure downstream of the bifurcation. Also shown is a comparison between
laser Doppler anemometry (LDA) measurements made at UIC and our preliminary spectral element
results. These results were obtained using a conforming spectral element discretization, which implies
that the mesh resolution is essentially uniform throughout the domain. While the agreement of these
preliminary results is impressive, this preliminary computation is lacking in several respects. First, the
mesh construction was quite time consuming, requiring several iterations amongst a team of experts.
Second, the mesh is suboptimal from the standpoint of point distribution and surface smoothing. Third,
the mesh resolution is essentially uniform throughout the domain, despite the fact that the turbulent region
(where high resolution is required) occupies less than ten percent of the domain. Finally, if this mesh
were used to undertake a full range of three cardiac 3 cycles, the simulation would require roughly 120
days on a typical 32-processor machine. Fortunately, because the spatial resolution required in the
turbulent region is roughly two to four times greater (in each direction) than required elsewhere, localized
refinement offers a potential for one- to two-orders of magnitude computational savings. For hexahedral
elements, an efficient way to achieve this localization is through oct-refinement of each element, as
illustrated in Fig. 2. Development of this capability in the context of our parallel spectral element code
will be a major component of this project

In addition to the meshing issues, we will investigate the potential for multigrid-based iterative solvers,
which have the potential to further reduce solution time. Although some research in spectral element
multigrid was undertaken in the early „90s, the method has not been adapted by anyone in the spectral
community. We expect that we‟ll be able to leverage our work in overlapping-Schwarz preconditioners
to address the shortcomings of earlier proposals in this area. In addition, we intend to commence
development of basic fluid-structure interaction capability. Presently, only a few groups are undertaking
the combined flow and vessel-wall problem. Early results indicate that in the regions of interest, which
feature high flow rates, the effect of wall motion has roughly a 10% impact on the wall shear stress
magnitude, with considerably less impact on the location of the peak. However, it appears that capturing
this component of the physics may be important for gaining medical acceptance of simulation results, and
there is a general trend in this direction within the CFD community.

Finally, it is important that the computational results be delivered to the physician in a readily accessible
and comprehensible format. The natural medium for this is html (or more flexible variants, e.g., xml).
An important component of this work will be to automate the data analysis for this particular problem
class, so that translation of the numerical output (the pressure and velocity fields) to the relevant clinical
data will be fully automated. Time averaged and rms plots of wall shear stress will be posted on a secure
website in a manner that will allow ready interpretation of the patient‟s condition, perhaps with some
degree of interactivity such as rotation of the viewing angle or contour threshold selection. This work
will most likely be carried out by summer students from nearby computer science departments.

                                                                                00      /s
                                                                                      5m /s

                                          -6 .6
                                           -6         -0.4
                                                        -0.4    0.4
                                                                 0 .4    .2
                                                                        11.2    22    2.8
                                                                                       2.8    3.6
                                                                                               3.6    4.4

                        (a)                                                     (c)                          (e)

                                                                                00     0 /s
                                                                                       .5m /s
                                                                                      0 .5m

                                          -6 .6
                                            .6          -0.4
                                                      -0.4       0
                                                                0.4.4    1.2
                                                                        1.2      22    2.8
                                                                                      2.8      3.6
                                                                                              3.6      4.4

                        (b)                                                     (d)                          (f)
                                                                   0   0.5m/s    0     0.5m/s
Figure 1. Spectral element mesh of AV-graft geometry (a); computed instantaneous vorticity contours downstream
of graft juncture (b); LDA measurements of time averaged velocity vectors (c) and turbulence intensities, u-rms (d);
and spectral element computation of time averaged velocity vectors (e) and turbulence intensities (f).
                                          -6 .6
                                            .6         -0
                                                          .4     0
                                                                   .4    1.2
                                                                        1.2      2

                                                                                 0     00 y e /c m
                                                                                         0d y e /c 2
                                                                                      3 000d n s m 2

                                           -6.6         -0 .4     0.4     1.2     2     2.8     3.6    4.4
                                          -6.6         -0.4      0.4     1.2     2     2.8     3.6    4.4

Figure 2. Centerplane cut illustrating a nonconforming (oct-refined) spectral element mesh with resolution
concentrated in the turbulent region of an AV-graft model.

Deliverables and Milestones:

Deliverables: i.       Software tool for automated generation of optimized computational meshes
                       from MRI/CT images

                ii.    Software tool for rapid determination of hemodynamic forces and particle
                       residence times from MRI/CT image and flow data

Year 1 Milestones:      i.    Automate translation of bifurcation images in to computational meshes
                      ii.     Develop and test hexahedral mesh smoothing criteria and software
                      iii.    Implement spectral element multigrid
                      iv.     Develop nonconforming spectral element code to allow localized refinement
                      v.      Develop and test spectral element mesh refinement criteria
                      vi.     Automate post-processing for wall shear stress computation (HTML output)
                      vii.    Develop and test basic fluid-structure interaction capabilities
                      viii.   Submit first simulation paper on turbulent flow induced by carotid stenoses

Year 2 Milestones:      i.    Automate hexahedral mesh smoothing and optimization
                      ii.     Automate nonconforming refinement (adaptive mesh refinement)
                      iii.    Automate post-processing of particle residence time computation
                      iv.     Implement initial fluid-structure capability in parallel SEM code

(5) Resources required (dependencies, key skills, new hires)

We will hire a post-doctoral researcher in the area of structural mechanics who has experience with
dynamic structural analysis. Many of the techniques in this area are quite similar to those used in fluid
mechanics, including the areas of mesh generation, iterative solvers, and high-performance computing.
The expertise on the structural mechanics side will greatly strengthen our position within this discipline.

The project will require access to the 512-processor Linux cluster in MCS.

(6) Future funding opportunities (direct follow-on and related programs) for next year and
subsequent years

Computational biofluids research is likely to become a core thrust area of the new ANL/UC Computation
Institute. NIH has a major forthcoming initiative in biomechanics, and we expect several additional
agencies such as NSF and NASA to soon recognize and plan for related programs. In addition, a recent
report by Alan Wolsky of ANL indicated that there may be $4 million budgeted in DOE‟s Division of
Medical Science for bioengineering research.

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